This week I learned about finding the relationship between two quantities, domain and range and the independent and dependent variables. In this lesson I struggled the most with domain and range and I’m still reviewing to understand it. In the photo above, it represents the different ways a relation can be written. These different ways include, table of values, mapping diagram, ordered pairs and a graph.

In order to know which is the dependent variable and which is the dependent variable you must know the input and output values, which is easy to determine! The input value is always on the left side of the table of values, mapping diagram and ordered pairs, and is the values on the x-axis, when looking at a graph.

There is also times when you are only given the input value and need to determine the output value with a certain equation given.

For example: y=2x-3

To find ‘y’ you would replace ‘x’ with the input value that you are given. In the photo below I provided a visual to determine the value of ‘y’ when you have an input value of 6.

Something I’ve learned this week was multiplying polynomials using the FOIL technique. FOIL is a type of distributive property.

FOIL stands for – i,e (a+b)(c+d)

First term in each bracket (ac)

Outside terms (ad)

Inside terms (bc)

Last term in each bracket (bd)

For example:

(x + 6)(x + 4)

= + 4x + 6x + 24

Once you solved the multiplication after foiling, you the collect “like terms’

(x + 6)(x + 4)

= + 4x + 6x + 24

=  + 10x + 24

Down below I included a picture that has arrows connecting the terms you multiply together.

I didn’t have any challenges with this chapter yet because it is mainly the same things that I did last year during polynomials in Math 9.

 

 

During trigonometry I learned how to find a missing angle using sin, cos or tan and the side lengths given. In the example that I’ve inserted, I used sin to figure out angle x. In order to find an angle in a right angle triangle you must have 2 out of the 3 side lengths. To determine what trig function to use you start out by labeling each side as opposite (opposite side of the angle you are trying to find), the hypotenuse (the side across from the right angle/the longest side of the triangle, and the adjacent (the side left over / the same side as the angle). Since I was only given the opp and hyp I would use sin (Soh Cah Toa helps me remember). To calculate the final answer you would punch in ” ” on your calculator.

In the beginning I had challenges on what way to use the trig functions ( sin or ) and where to put the given information in word problems. By the end of the chapter I completed enough review to fully understand what to do.

I learned about finding the surface area and volume of prisms, cylinders, pyramids and cones. Above I have an example of find the SA and V of a cone. Each shape has its own formula so its mostly based around which one to use and plugging in the correct numbers. Looking at the diagram, it only gave me the vertical height and slant height so I had to use Pythagorean theorem to figure out the radius. Once you have all the measurement required you then solve by replacing the r, h and s with the actual numbers.

The challenges I had with this was mostly with word problems, because sometimes I was unsure of what measurements go where and what to include and what not to include. Overall this was a fairly simple chapter once I did enough review that I needed.

I learned how to convert units from the SI system to the imperial system and from imperial to SI. In the example given, I am converting 208 inches into meters using unit analysis. Depending on what units you are converting, you may have to go through multiple conversions. For me, I had to convert inches to centimeters and then centimeters to meters. When converting and cancelling out a unit, you need to make sure that unit is on the numerator and then again on the denominator, as you can see in the example.

Something new that I learned in math this week was solving equations with negative exponents, this includes fraction exponents and negative exponents in fraction form. Basically, what I learned was how to convert the negative exponents into positive and solve the equation accurately. In the picture above it shows an equation that is similar to the ones that I solved in class, it also includes a step by step procedure so you can see how to do it properly.